Simplify the following expression: $r = \dfrac{9}{5x} + \dfrac{1}{9x}$
In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $5x$ and $9x$ $\lcm(5x, 9x) = 45x$ $ r = \dfrac{9}{9} \cdot \dfrac{9}{5x} + \dfrac{5}{5} \cdot \dfrac{1}{9x} $ $r = \dfrac{81}{45x} + \dfrac{5}{45x}$ $r = \dfrac{81 +5}{45x}$ $r = \dfrac{86}{45x}$